On the number of representations of natural numbers by cyclic binary quadratic forms (Q2862889)
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scientific article; zbMATH DE number 6228973
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the number of representations of natural numbers by cyclic binary quadratic forms |
scientific article; zbMATH DE number 6228973 |
Statements
19 November 2013
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binary quadratic forms
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theta series
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Hecke operators
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On the number of representations of natural numbers by cyclic binary quadratic forms (English)
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The author states a general formula for the number of representations of natural numbers by binary quadratic forms of negative discriminant. The formula for a form \(f\) depends on the values of characters of the class group at the class containing \(f\), and involves basic information about a suitable theta series. No hint is given about the proof nor about the source where the proof has been published. The main concern of the author is to analyze this general formula in the case when the class group is cyclic. In this special case a simplified version is obtained not involving the machinery of theta series.
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